Although generalized Delaunay triangulations using arbitrary convex shapes are known to be spanners, their spanning ratios are less well understood. Tight bounds on the spanning ratio are only known when an equilateral triangle, a square, or a regular hexagon is used in the construction. When using equilateral triangles, Chew [1]} showed that the spanning ratio is 2. When using squares, Chew [2]} showed an upper bound of \(\sqrt{10} \approx 3.16\) , and Bonichon et al.  [3]} showed a matching upper and lower bound of \(\sqrt{4 + 2 \sqrt{2}} \approx 2.61\) . When using regular hexagons, Perković et al.  [4]} showed a tight bound of 2.
